Kirkuk and Tikrit are seen as the militants' major strongholds east of the Tigris river.

Carpet-bombing 'not the answer'

As the battles continued, Iraqi Defence Minister Khalid al-Obeidi said his country was comfortable receiving military aid from Iran as well as from the US.

"We are in dire need because we are at war," he said during a visit to Iraq by the top US military commander, Gen Martin Dempsey. "I think the situation is balanced."

Gen Dempsey meanwhile appealed for "strategic patience" in the campaign against IS, stressing that "underlying issues" - such as strengthening the Iraqi army and reducing Sunni Arab alienation - had yet to be resolved.

"Carpet-bombing through Iraq is not the answer," he said.

The US began air strikes against IS after the jihadist militants seized a broad belt of territory across Syria and Iraq last year.